Events for 04/22/2022 from all calendars

Noncommutative Geometry Seminar

Time: 08:00AM - 09:00AM

Location: ZOOM

Speaker: Yuguang Shi, Peking University

Title: Quasi-local mass and geometry of scalar curvature

Abstract: Abstract: Quasi-local mass is a basic notion in General Relativity. Geometrically, it can be regarded as a geometric quantity of a boundary of a 3-dimensional compact Riemannian manifold. Usually, it is in terms of area and mean curvature of the boundary. It is interesting to see that some of quasi-local masses, like Brown-York mass, have deep relation with Gromov’s fill-in problem of metrics with scalar curvature bounded below. In this talk, I will discuss these relations. This talk is based on some of my recent joint works with J.Chen, P.Liu, W.L. Wang , G.D.Wei and J. Zhu etc.

URL: Event link

Noncommutative Geometry Seminar

Time: 09:15AM - 10:15AM

Location: ZOOM

Speaker: Jintian Zhu, Peking University

Title: Incompressible hypersurface, positive scalar curvature and positive mass theorem

Abstract: In this talk, I will introduce a positive mass theorem for asymptotically flat manifolds with fibers (like ALF and ALG manifolds) under an additional but necessary incompressible condition. I will also make a discussion on its connection with surgery theory as well as quasi-local mass and present some new results in these fields. This talk is based on my recent work joint with J. Chen, P. Liu and Y. Shi.

URL: Event link

Working Seminar on Banach and Metric Spaces

Time: 10:00AM - 11:30AM

Location: BLOC 302

Speaker: Florent Baudier, Texas A&M University

Title: Coarse rigidity of uniform Roe algebras

Mathematical Physics and Harmonic Analysis Seminar

Time: 1:50PM - 2:50PM

Location: BLOC 302

Speaker: Giorgio Young, Rice University

Title: Ballistic Transport for Limit-periodic Schrodinger Operators in One Dimension

Abstract: In this talk, we will discuss recent work examining the transport properties of the class of limit-periodic continuum Schr\"odinger operators whose potentials are approximated exponentially quickly by a sequence of periodic functions. For such an operator $H$, and $X_H(t)$ the Heisenberg evolution of the position operator, we show the limit of $\frac{1}{t}X_H(t)\psi$ as $t\to\infty$ exists and is nonzero for $\psi\ne 0$ belonging to a dense subspace of initial states which are sufficiently regular and of suitably rapid decay. This is viewed as a particularly strong form of ballistic transport, and this is the first time it has been proven in a continuum almost periodic non-periodic setting. In particular, this statement implies that for the initial states considered, the second moment grows quadratically in time.

Algebra and Combinatorics Seminar

Time: 3:00PM - 4:00PM

Location: Zoom

Speaker: Anton Bernshteyn, Georgia Tech

Title: Lower bounds for difference bases

Abstract: A difference basis with respect to $n$ is a subset $A \subseteq \mathbb{Z}$ such that $A - A \supseteq [n]$. R\'{e}dei and R\'{e}nyi showed that the minimum size of a difference basis with respect to $n$ is $(c+o(1))\sqrt{n}$ for some positive constant $c$. The precise value of $c$ is not known, but some bounds are available, and I will discuss them in this talk. This is joint work with Michael Tait (Villanova University).